( 807 ) 
with a great number of degrees of freedom, it is very difficult to say 
in general. It appears to me that it will be very rare in any case 
for a system which is in a “molekular ungeordnet” state to pass to 
a “molekular geordnet” one. 
Meanwhile a circumstance appears which is favourable for the 
hypothesis of Hertz and Einstein. Though many phases may exist 
that cannot be attained by a determined path, these phases can 
be indiscernible for observation, for we shall find the same observed 
data for systems widely differing in internal state. Taking together 
all these “equivalent” states and paths, we get an important extension 
of the ensemble which can be used to deduce something about the 
observed quantities. And though there is, strictly speaking, no direct 
connection between the systems taken into account, our results may 
teach us something of the systems of observation. 
Another favourable circumstance is that a great part of the systems 
of a microcanonical ensemble differ very little. The same is true for 
the states which a system successively passes through. The system, 
equivalent to the greater majority of the states consecutively passed 
through, may be the same as that which is equivalent to the majority 
of the systems of a microcanonical ensemble. (The same is true for 
a canonical ensemble). 
Prudence is however recommended not to generalise this result. 
Take for example the case of a large number of perfectly smooth 
and rigid spherical molecules enclosed in a spherical vessel, which 
walls are supposed pertectly elastic and smooth with respect to the 
molecules. The resulting moment of momenta with respect to the 
centre is now constant. If an initial state has been given the coor- 
dinates of the representing point are limited by the equations 
CA 
ed 
é 
M 
| 
= 
M is a known function of the coordinates and the momenta. The 
path of the system will now be confined, to the 2 (n— 1)-dimensional 
space (2), points of 5, lying outside (2) are never reached. For 
the majority of the systems possessing a given energy however the 
moment J/ will differ only little from O. If one divides the space 
Em-1 by spaces 1 =—0, M=d... in layers, then the majority of 
the systems will be situated in the layer (M =0... M= 4), where 
J is a very little quantity. The systems of each layer will be equi- 
valent for the greater part. Though the path of the representing 
point may not pass through all the points, we shall find results of 
